4.5 Dividing Decimals and Order of Operations
Learning Objectives:
1. Divide decimals.
2. Divide decimals by powers of 10.
3. Applications involving dividing decimals.
4. Review and use order of operations to simplify expressions containing decimals.
A. Dividing decimals
Steps for Dividing a Decimal by a Whole Number:
1. Place the decimal point in the quotient directly above the decimal point in the dividend.
2. Divide as with whole numbers.
Example 1. Divide.
26 7.826
Steps for Dividing a Decimal by a Decimal:
1. Move the decimal point in the divisor to the right until the divisor is a whole number.
2. Move the decimal point in the dividend to the right the same number of places as the decimal
point was moved in step 1.
3. Divide. Place the decimal point in the quotient directly over the moved decimal point in the
dividend.
Example 2. Divide.
8.9 22.25
B Dividing by Powers of 10
To Dividing a Decimal number by 10, 100, 1000, or a higher power of 10—is to move the
decimal point as many places to the left as there are zeros in the power of 10 being divided
Example 3. Divide.
1.
7.74
10
2.
1.047 ÷ 100
C.
Solving Problems by Dividing Decimals
Example 4. A square feet bag of fertilizer covers 1250 square feet of lawn. Time Parker’s lawn
measures 14,800 square feet. How many bags of fertilizer does he need? If he can buy
only whole bags of fertilizer, how many whole bags does he need?
E.
Simplifying Expressions with Decimals
Example 5. Simplify each expression.
1.
0.1558 ÷ 0.02 · 4.45
2.
(3.6) + 4.5 – 8.7
2